the graph shows a distribution of data. which statement about the data is true? the data has a standard…

Explanation:

Step1: Recall normal - distribution properties

In a normal distribution, about 68% of the data lies within 1 standard deviation of the mean, about 95% lies within 2 standard deviations of the mean, and about 99.7% lies within 3 standard deviations of the mean. Without knowing the mean and standard deviation exactly from the graph, we assume a standard normal - like distribution centered around 0.5 (since the graph is symmetric around 0.5).

Step2: Analyze each option

• Option 1: There is no information to suggest that the standard deviation is 0.1.
• Option 2: There is no information to suggest that the mean is greater than 0.5.
• Option 3: If the mean is 0.5 and we assume a reasonable spread, a value of 0.7 is not within 1 standard deviation of the mean. In a normal distribution, if the mean is (\mu = 0.5), for a value (x = 0.7), (|x-\mu|=0.2). If the standard - deviation (\sigma) is such that the distribution is symmetric around 0.5, and considering the shape of the curve, 0.7 is more than 1 standard deviation away from 0.5.
• Option 4: If the mean is 0.5, for a value (x = 0.9), (|x - \mu|=|0.9 - 0.5| = 0.4). In a normal distribution, if we assume a non - zero standard deviation (and the spread of the graph), a value of 0.9 is more than 2 standard deviations from the mean. For example, if we assume a "standard" normal - like spread where about 95% of the data is within (x=\mu\pm2\sigma), and (\mu = 0.5), values beyond 0.9 (if (\sigma) is reasonable) are more than 2 standard deviations from the mean.

Answer:

A value of 0.9 is more than 2 standard deviations from the mean.